Better mathematics boosts image-processing algorithm

A MATHEMATICAL tool named for its speed just got thousands of times faster. The blistering new version of the fast Fourier transform (FFT) should make compressing audio and video less of a drain on mobile devices.

The Fourier transform, which splits a signal into its individual pure frequencies, was devised over 200 years ago but only became practically useful after the development of the FFT, a short cut, 60 years ago. Among other things, the FFT is used in compression algorithms that efficiently store audio and video.

Now computer scientist Dina Katabi and colleagues at the Massachusetts Institute of Technology have developed a new FFT that is much, much faster.

Signals used in technologies such as Wi-Fi are designed to fully exploit all available frequencies, so they tend to be made up of a wide range of pure frequencies, which all contribute equally. By contrast, images and music tend to be dominated by a small number of frequencies. The team improved performance on boiling down these "sparse" signals.

They created a more efficient way to filter a sparse signal by dividing the range of frequencies into sets and identifying which sets contained important frequencies. Then they pinpointed this frequency within each of these sets.

This can be done by subdividing the set repeatedly until only the important signal remains, but the researchers chose a technique normally used in wireless communications. It exploits the fact that the most important frequency modulates the signal more than any of the other frequencies in the set. Sampling the set rapidly at different times reveals this dominant frequency. The method processes sparse signals up to 10,000 times faster than the old FFT, say the team.

This could improve battery life on mobile devices. "If the algorithm does fewer operations then it consumes less power," Katabi says. The work was presented at the Symposium on Discrete Algorithms in Kyoto, Japan, last week.

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